The French champions are looking to bolster the squad next season, which includes the goalkeeping department.
The Sun have now reported that the PSG are tracking De Gea's situation in Manchester with the hoping of making a move in the off-season.
PSG manager Mauricio Pochettino is believed to be looking for a new number one to replace three-time UEFA Champions League winner Keylor Navas.
The club had been linked with Tottenham Hotspur shot-stopper Hugo Lloris in recent months, but it appears the United goalminder has been PSG's radar for some time now.
The report claims that the Paris outfit are one of the few clubs in Europe who could take on De Gea's £375,000-a-week wages while still offering a fee for his services.
The Spaniard still has two years remaining on his current deal at Old Trafford, where he is reportedly the highest-paid player.
The Sun also reported that United are set let one of their top goalkeepers, with Dean Henderson pushing for more regular minutes after some impressive cameos.